where \(\hat{b}_{k}\)  is the \(k\) th mean component of the mixture model and \(b^\text{gt}\)  is the corresponding ground truth bounding box.
Afterwards, we update the parameters of the \(k^*\)  component following the approach proposed in [1]},
\( \mathcal {L}_{\text{box}} = \sum _{n} \frac{1}{\hat{\sigma }_{k^*}} \left|\hat{b}_{n, k^*} - b_n^\text{gt} \right| + \log \hat{\sigma }_{k^*}\) 
